Convergence of Runge–Kutta methods for nonlinear parabolic equations Original Research Article

In this paper, we study time discretizations of fully nonlinear parabolic differential equations. Our analysis uses the fact that the linearization along the exact solution is a uniformly sectorial operator. We derive smooth and nonsmooth-data error estimates for the backward Euler method, and we prove convergence for strongly A(ϑ)-stable Runge–Kutta methods. For the latter, the order of convergence for smooth solutions is essentially determined by the stage order of the method. Numerical examples illustrating the convergence estimates are presented.